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1
Glacier hydrology
Thomas SchulerDepartment of [email protected]
GEO 4420, 19.10.2006Glacier hydrology
Relevance:• Water resource (climate change scenario)
• Ice dynamics (sliding, surge, icestreams)
• Geo-hazards (outburst floods)
• (Erosion, sediment transport)
2nd part: applied glaciology
Glacier hydrologywater sources(not treated)
water movementthrough a glacier
characteristics of glacial runoff
hydrologist
Water sources
Topography, geologyInflow from surroundings, groundwater
Climate, topographyRain
• surface energy balance• ice deformation• sliding velocity, geothermal heat flux
Melt-water:• surface ~0.1-10 m a-1
• internal• basal
ControlSource
} 0.01 m a-1
2
Glacier runoff and climate change
Q ?
Characteristics: Seasonal Variation
Jan Mar May Jul Sep Nov Jan0
1
2
3
4
Pard
é-co
effic
ient
Seine (Paris)'Oceanic'
Dnjepr (Kamenka)'Snow'
Rhone (Gletsch)'Glacier'
Characteristics: Summary
Annual runoff
Seasonal variation
Diurnal variation
Year-to-year variability
Runoff correlation
Aperiodic variations
Decrease for pos mass balIncrease for neg mass bal
Runoff concentration duringmelt season
Pronounced diurnal cyclicity
Reduced at moderate glacierization’Glacier compensation effect’
Outburst floods
Pos. correlation with tempNeg. correlation with precip
VARIABLE CHARACTERISTICVernagtferner 1992
3-Jan 3-Mar 2-May 1-Jul 30-Aug 29-Oct 28-De0
2
4
6
8
10
Dis
char
ge (m
3 /s)
0 20 40 60 80 1000.10
0.15
0.20
0.25
Characteristics: Diurnal Variation Vernagtferner 1992
16-Jul 21-Jul 26-Jul 31-Jul 5-Aug 10-Aug0
2
4
6
8
10
Dis
char
ge (m
3 /s)
Seasonal evolution: 1. Increase in meltwater production
(Lower albedo due to more ice at surface)Increase in amplitude
2. Increase in efficiency of water transportFaster arrival of peak discharge
3
Response to warming: Annual runoff
Q P E G S= − + −∆
Jansson et al. 2003
Glacier hydrologySLOW
• ~ 0.5 m/h• ~ Porous ground
water aquiferFAST
• ~ 0.5 m/s• ~ Karst aquifer
Response to warming
Hock et al. 2003
VERNAGTFERNER
19781998
19-Jul24-Jul
29-Jul3-Aug
8-Aug13-Aug
18-Aug23-Aug
28-Aug0
4
8
12
Dis
char
ge (
m3 s-1
)
Photos: Schuler
Response to warming: Diurnal Variations
4
Response to warming: Summary
Specific runoff
Seasonal variation
Diurnal fluctuation
Year-to-year variability
Runoff correlation
Increase Decrease
Reduced runoff concentrationProlongation of melt season
Increase Decrease
Increase or decrease Increasedepending onInitial glacierization
Increased pos corr Decreasedwith temp
VARIABLE CHANGE UNDER CLIMATE WARMING
Initial stage Later stage
Glacier hydrologywater sources(not treated)
water movementthrough a glacier
characteristics of glacial runoff
Hydrologist/ glaciologist
Subglacial drainageRöthlisberger channel (R-channel) Röthlisberger, 1972
• Enlargement due to frictional heating• Closure due to ice deformation
dynamic channel geometryseasonal evolution !
• Steady-state:Pw ~ Q-b
inverse pressure-discharge relationshiparborescent structure !!
Drenering gjennom isen
Friksjon skaper varme
Varme smelter is
Stream channels On Vibeke Gletscherin East Greenland, Photo: M. Hambrey
5
Drainage systems and water pressure
courtesy: U.H. Fischer
Channelized drainage systems
Röthlisberger Hooke Nye Walder & Fowler
• hydraulically efficient (variable pressure)• dynamic geometry (dependent on water flux)• arborescent structure (localized feature)
Linked cavity system Subglacial sediment
Water film
Distributed drainage systems
Kamb, 1987
Boulton, 1974
Weertman, 1972
• Hydraulically unefficient (high pressure)• Stable features (no evolution)• Non-arborescent structure (distributed)
Drainage systems and water pressure
courtesy: U.H. Fischer
6
Relevance to ice dynamicsdtotal = ddeformation + dbasaldtotal
ddeformation
dbasal
pw
sliding law:
vbasal ~ (pi -pw)-1}
effective pressure
glacier
lake
outlet
hi
seal (?)
hw
distance x
Special case: jøkulhlaup
• Water masses dammed by a glacier• Dam-stability controled by ice-thickness and filling level• Outbursts may occur periodically and cause destructive floods
( ) ( )n
w
i
w hhn
gABxz
xhtQ
LgC
dtdA
⎟⎠⎞
⎜⎝⎛ −−−+⎟
⎠⎞
⎜⎝⎛
∆∆
+∆∆
−= *2transfer)heat(1)( ργρρ
Time-dependent geometry of an ice-walled conduit:
Nye, 1976; Spring & Hutter, 1982; Clarke, 1982; Ng, 1998; Clarke, 2003
Modeling discharge through a R-channel
size melt-enlargement creep-closure
Model results: jøkulhlaup
glacier
lake
hihw
lake level evolution
flood hydrograph
channel evolution
7
Instability of channelized drainage
ice-dammed lake glacier
subglacial channel
glacier snout:outlet portal
Jøkulhlaup in Norway
Photos: Hjelmaas
Apr04 Jul04 Oct04 Jan05 Apr05 Jul05 Oct05
26/08/05 28/08/05 30/08/05 01/09/05 03/09/05 05/09/050
10
20
30
40
50
60
wat
er le
vel (
m) 10
20
30
40
50
water level(m
)
vannstand Øvre Messingmalmvatn
~ 1000 m3 s-1
geofonutslag
Blåmannsisen jøkulhlaup 2005
8
Case study: Applied glacier hydrology at Høganesbreen
Can water intrusions in a mine beneathHøganesbreen be evacuated subglacially?
SNSK requested recommendations from UiO
Coal mining in Svea
??mine
Gruvefonna
Problem: water intrusions troublemining activities beneath the glacier
Høga
nesb
reen
During summer Q max ~50 000 m3 d-1
Pumping the waterfrom the mine isexpensive
??mine
Gruvefonna
Høga
nesb
reen
Can water intrusions in the mine be evacuatedsubglacially?
drainage tunnel??
Idea: drainage tunnel to the bed of Høganesbreen
9
Strategy
• Can we expect a channelized drainage system in the region where the tunnel should connect to the glacier bed?(hydraulic potential mapping surface & bedrock topography)
• If so, will the water drain gravitationally away from the mine?(R-channel model
glacier geometry, ice temperature & water discharge)
Bedrock topography by radar
upper part of Høganesbreen in the area of theplanned drainagetunnel
Interpolation of ice-thickness
measurements
and constructionof a bedrock map Direction of water flow
From experience:• Water flow follows the
topographic gradient
and• Water flows from high
pressure to lowerpressurepump
(high pressure)
10
Hydraulic potentialDefinition: Φ = ρw g z + pw
Alternative: express Φ in terms of water column H = z+h, pw=ρwgh)
principles: water flows from higher to lower potential
flow is perpendicular to isopotential lines
Hydraulic potential mapping
Assume: pw= f pi = f ρigh, f є [0,1]h
f = 1.0 f = 0.5 f = 0.0
( ) ( )n
w
i
w hhn
gABxz
xhtQ
LgC
dtdA
⎟⎠⎞
⎜⎝⎛ −−−+⎟
⎠⎞
⎜⎝⎛
∆∆
+∆∆
−= *2transfer)heat(1)( ργρρ
Time-dependent geometry of an ice-walled conduit:
Nye, 1976; Spring & Hutter, 1982; Clarke, 1982; Ng, 1998; Clarke, 2003
Modeling discharge through a R-channel
size melt-enlargement creep-closure
Model input: water discharge in the mine(estimated from pump rates)
0 50 100 150 200time (d)
short artic melt saison
Two scenarios were calculated using different flow law parameters for the ice
11
Model results: pressure evolution in theartificial drainage tunnel
• Even in an extreme case,open-channel conditionswill last for less than twomonths
• Under pressurized conditions,water would drain into ratherthan away from the mine
We recommendNOT to proceed withthe construction of an artificial drainagetunnel
Will the amount of water input increasewith the enlargementof the mine?
And, if so, can weestimate how much?
future mining areawill be significantly
enlarged
Water transfer from the glacier to the mine
bedrock underneath the glacierdisturbed by collapsing mine
12
Approach
Melt-water production, spatially distributed
Monitoring of water discharge in the mine
Transfer modelglacier surface – mine
Future evolution of melt-water intrusions (total volume, peak discharge)
M = (MF + aice/snow*DIR) * T+
(Hock, 1999)
Records of pump rate
Melt model validation
Model results
Svea Nord
Contributing glacier surface?1) Perfect and directvertical water transfer
2) Lateral water influx along theglacier bed (hydraulic potential surface)
Svea Nord
13
Results
Modeled melt production (1.7*106
m3) accounts only for 60% of measured discharge(2.8*106 m3)
Subglacial catchmentDistribution of subglacial hydraulic potential based on maps of bedrock topographyand glacier surface:
H = z + ρi / ρw hi
Mapping the subglacial catchment area for the actualmine and several steps of future enlargement
Calculated melt water volume(2.85*106 m3) agrees withmeasured discharge(2.83*106 m3)
Transfer glacier mine
melt water production
measured discharge
simulated discharge (k=14d)
surface melt water + rain linear reservoir mine discharge
Prediction
With the enlargement of the mine, the volume of water intrusionswill progressively increase up to 3.5 times of the actual value.Diurnal peak discharge will increase similarly(54*103 m3 s-1 190*103 m3 s-1).
14
Summary of results• Calibrated melt model (80% accuracy)
• Delineation of the subglacial catchment area usingsubglacial hydraulic potential.
• Transfer glacier mine can be described using a linear reservoir approach (k = 14 d).
• The model predicts a progressive increase of the water intrusions up to a factor of 3.5 with enlargement of the mine.
• The scenarios are based on meteo data from 2003 and assume parameter values being constant. Thus, the actual form of the hydrograph will vary from year to year (according to weather pattern).
Where does all this Where does all this water come from??water come from??
Comparison meteo data
Mass balance from stake readings:
2003: ~-1200 mm w.e.
2004: ~-1400 mm w.e.
Probably slightly more melt in 2004
15
2003
2005
Model explains ~50% ofobserved water volume
Svea Nord
Can increase in permeability enlarge the catchment area?
?
Model structure
Meltwater production & routing at surface
Englacial storage
Subglacial watersheet
Groundwater
Exchange controled by gradient in hydraulic potential
Model structure
Sveagruva
Meltwater production & routing at surface
Englacial storage
Subglacial watersheet
Groundwater
Distributed melt model
Continuity & Darcy physics(nonlinear conductivity)
Exchange controled by hydraulic potential gradient
Continuity & Darcy physics
Continuity & Darcy physics(nonlinear conductivity)